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# If a circus sells all of its 220 tickets for this month's performance

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Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
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manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4

We can let p = the usual price per ticket and r = revenue last month

So the normal revenue would be 220p and we can create the equation:

220p = 1.1r

200p = r

When the ticket price is raised 5%, the revenue is 1.05p(200) = 210p.

So the percent change from last month would be (200p - 210p)/210p x 100 = -10/210 x 100 = -1000/210 = -100/21, which corresponds to a revenue that is 100/21 percent less than this month’s revenue.

Answer: C
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Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
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Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
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manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4

If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month.
For the usual ticket price to yield 10% more in revenue, the number of tickets sold this month must be 10% greater than the number sold last month.
Since 220 is 10% greater than 200, the number of tickets sold last month = 200.

If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
Since the number of tickets sold is the same as that sold last month -- 200 -- raising the ticket price by 5% will increase the total revenue by 5%.
Let last month's revenue = $100, implying that the revenue yielded by this month's 5% higher ticket price =$105.
Percent decrease from 105 to 100 $$= \frac{Difference}{Original }* 100 = \frac{5}{105} * 100 = \frac{100}{21}$$

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Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
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manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4

let price per ticket be 100$and 5% increase ; 105$
220*100 ; 220,00 last year revenue must be 220,00/1.1 ; 200,00 $with price increase$105 tickets sold 200 ; 21,000
21000-20000/21000 ; 1000/21000 ;1/21*100
option C ; 100/21
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Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
manalq8
Given: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month.
Asked: If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
Let the ticket's usual price be p.

Tickets sold this month = 220 tickets
Revenue this month = 220p

Revenue last month = 220p/1.1 = 200p

Ticket price after raising by 5% = 1.05p
Revenue after selling 200 tickets = 1.05p*200 = 210p

Difference in last month's revenue and this month's revenue = 210p - 200p = 10p
The percent less would last month's revenue be compared to this month's revenue = 10p/210p *100 = 1000/210 = 100/21%

IMO C
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Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4

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­Lets assume the cost per ticket is $x. Total revenue earned =$ 220x
This months revenue was 10% greater than last months

Last months revenue = $220x / 1.1 =$200x

Revenue earner for 200 tickets at 5 % increase in price = \$ 200x* 1.05
Percentage = (200x*1.05 - 200x)/(200x*1.05)*100
= 100/21
Re: If a circus sells all of its 220 tickets for this month's performance [#permalink]
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